THE CATENARY DEGREE OF KRULL MONOIDS II

DOI10.1017/S1446788714000585zbMath1373.20074arXiv1407.0548MaRDI QIDQ5253332

Qinghai Zhong, Alfred Geroldinger

Publication date: 5 June 2015

Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.0548

zbMATH Keywords

zero-sum sequencesKrull monoidssets of lengthscatenary degreesets of distancesnonunique factorizations

Mathematics Subject Classification ID

Units and factorization (11R27) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Sequences (mod (m)) (11B50) Divisibility and factorizations in commutative rings (13A05) Inverse problems of additive number theory, including sumsets (11P70) Arithmetic theory of semigroups (20M13)

Related Items (14)

Factorization invariants of the additive structure of exponential Puiseux semirings ⋮ On length densities ⋮ The set of distances in seminormal weakly Krull monoids ⋮ A characterization of class groups via sets of lengths ⋮ On monoids of weighted zero-sum sequences and applications to norm monoids in Galois number fields and binary quadratic forms ⋮ Sets of arithmetical invariants in transfer Krull monoids ⋮ On the incomparability of systems of sets of lengths ⋮ On the algebraic and arithmetic structure of the monoid of product-one sequences ⋮ On Syzygies for Rings of Invariants of Abelian Groups ⋮ Minimal relations and catenary degrees in Krull monoids ⋮ Sets of minimal distances and characterizations of class groups of Krull monoids ⋮ A characterization of Krull monoids for which sets of lengths are (almost) arithmetical progressions ⋮ Which sets are sets of lengths in all numerical monoids? ⋮ Some Recent Results and Open Problems on Sets of Lengths of Krull Monoids with Finite Class Group

Cites Work

• Unnamed Item
• The catenary degree of Krull monoids. I
• Monoids of modules and arithmetic of direct-sum decompositions.
• Number theory of matrix semigroups
• Combinatorial number theory and additive group theory. With a foreword by Javier Cilleruelo, Marc Noy and Oriol Serra (Coordinators of the DocCourse)
• Arithmetical characterization of class groups of the form \(\mathbb Z/n\mathbb Z\oplus\mathbb Z/n\mathbb Z\) via the system of sets of lengths.
• Structural additive theory. Based on courses given at Karl-Franzens-Universität Graz, Austria, 2008--2012
• Sets of lengths in maximal orders in central simple algebras.
• Factorizations of upper triangular matrices
• The catenary and tame degree in finitely generated commutative cancellative monoids.
• Products of two atoms in Krull monoids and arithmetical characterizations of class groups.
• The catenary and tame degree of numerical monoids generated by generalized arithmetic sequences
• THE CATENARY AND TAME DEGREES ON A NUMERICAL MONOID ARE EVENTUALLY PERIODIC
• The set of distances in Krull monoids
• Inverse zero-sum problems II
• The catenary and tame degree of numerical monoids
• FACTORIZATION INVARIANTS IN HALF-FACTORIAL AFFINE SEMIGROUPS
• Factorization Theory and Decompositions of Modules
• Inverse zero-sum problems III

This page was built for publication: THE CATENARY DEGREE OF KRULL MONOIDS II